Singular perturbation problems for systems of partial differential equations of elliptic type

Elliptic boundary value problems for systems of nonlinear partial differential equations of the form $\text{F}{}_{\mathrm{i}}\text{(x, u}{}_1\text{, u}{}_2\text{,…, u}{}_{\mathrm{N}}\text{,}\text{?u}{}_{\mathrm{i}}\text{?x}{}_{\mathrm{j}}\text{, ?}{}^{\mathrm{p}}{}_{\mathrm{i}}\text{?}{}^2\text{u}{}_{\mathrm{i}}\text{?x}{}_{\mathrm{j}}\text{?x}{}_{\mathrm{k}}\text{) = ?}{}_{\mathrm{i}}\text{(x), x ? R}{}^{\mathrm{n}}$, i = 1(1)N, j, k = 1(1)n, p_i ? 0, ? being a small parameter, with Dirichlet boundary conditions are considered. It is supposed that a formal approximation Z is given which satisfies the boundary conditions and the differential equations upto the order χ(?) = o(1) in some norm. Then, using the theory of differential inequalities, it is shown that under certain conditions the difference between the exact solution u of the boundary value problem and the formal approximation Z, taken in the sense of a suitable norm, can be made small.     

Photoinduced macroscopic chiral structures in a series of azobenzene copolyesters

A study of the propagation of elliptically polarized light and the resulting formation of macroscopic chiral structures in a series of azobenzene side-chain copolyesters, in which the morphology is varied from liquid crystalline to amorphous, is reported. Real-time measurements are presented, showing the dynamic behavior of the photoinduced rotation of the polarization ellipse in the different samples. The relationship between the ellipticity of the recording light and the linear birefringence induced is studied. A numerical solution that takes into account the influence of the photoinduced linear dichroism on the light propagation through the samples is presented. Received: 10 June 2002 / Revised version: 26 July 2002 / Published online: 15 November 2002 RID="*" ID="*"Corresponding author. Fax: +45-4677/4588, E-mail: lian.nedelchev@risoe.dk RID="**" ID="**"Permanent address: Department of Chemistry and Physics, The Nottingham Trent Unversity, Clifton Lane, Nottingham NG11 8NS, England     

Sulfonated Poly(ether ether ketone) and Poly(ethylene glycol) Diacrylate Based Semi-Interpenetrating Network Membranes for Fuel Cells

Polymer electrolyte membranes are prepared from novel semi-interpenetrating polymer network material where the sulfonated poly (ether ether ketone) (SPEEK) is the linear polymer and the poly (ethylene glycol) diacrylate (PEGDA) is the cross-linking constituent. The semi-IPN is prepared by in situ polymerization of PEGDA in the presence of sulfonated poly (ether ether ketone). SPEEK is prepared by direct sulfonation of commercial PEEK (Gatone? 1100) by reported procedures. SPEEK with degree of sulfonation 63% (calculated from FT-NMR) is selected as the base membrane and different semi-IPN membranes were prepared by varying the PEGDA and SPEEK ratio. The degree of sulfonation of SPEEK and the formation of semi-IPN were confirmed by spectroscopy studies. The various semi-IPN membranes were characterized for ion-exchange capacity, water uptake, hydrolytic stability, proton conductivity and thermal stability for evaluating the suitability of these membranes for fuel cells. The proton conductivity of the membranes decreased with increasing PEGDA content. The Semi-IPN membranes exhibited conductivities (30°C) from 0.018 S/cm to 0.006 S/cm. These interpenetrating network membranes showed higher hydrolytic stability than the pure SPEEK membrane. This study shows that semi-IPN membranes based on PEGDA and SPEEK can be viable candidates for electrolyte membranes.     

Sodalite‐type Cu‐based Three‐dimensional Metal–Organic Framework for Efficient Oxygen Reduction Reaction

Inspired by copper‐based oxygen reduction biocatalysts, we have studied the electrocatalytic behavior of a Cu‐based MOF (Cu‐BTT) for oxygen reduction reaction (ORR) in alkaline medium. This catalyst reduces the oxygen at the onset (E_onset) and half‐wave potential (E^1/2) of 0. 940 V and 0.778 V, respectively. The high halfway potential supports the good activity of Cu‐BTT MOF. The high ORR catalytic activity can be interpreted by the presence of nitrogen‐rich ligand (tetrazole) and the generation of nascent copper(I) during the reaction. In addition to the excellent activity, Cu‐BTT MOF showed exceptional stability too, which was confirmed through chronoamperometry study, where current was unchanged up to 12 h. Further, the 4‐electrons transfer of ORR kinetics was confirmed by hydrodynamic voltammetry. The oxygen active center namely copper(I) generation during ORR has been understood by the reduction peak in cyclic voltammetry as well in the XPS analysis.     

Booster Method for Singularly-Perturbed One-Dimensional Convection-Diffusion Neumann Problems

An improved numerical method for singularly-perturbed two-point boundary-value problems for second-order ordinary differential equations subject to Neumann-type boundary conditions is proposed. In this method, an asymptotic approximation is incorporated into a finite-difference scheme to improve the numerical solution. Uniform error estimates are derived when implemented in known difference schemes. Numerical results are presented in support of the proposed method.     

Whirling and stability of flywheel systems,part II: Comparison of numerical results obtained with combined and lumped parameter models

In this paper the theoretical analyses of Part I are applied to some flywheel systems to provide information to designers. The analyses are utilized to study three specific prototype flywheel systems: a multi-material ring type (Garrett AiResearch), a constant-thickness-disk ring type (General Electric), and a tapered-thickness-disk type (Lawrence Livermore National Laboratory). In addition, the effects of the following flywheel design parameters on system dynamics are investigated: flywheel mass, flywheel diametral and polar mass moments of inertia, location of flywheel diametral and polar mass moments of inertia, location of flywheel mass center from the lower end of the quill shaft, quill shaft length, lower turbine-bearing support stiffness, and equivalent viscous damping coefficient of the external damper.     

Spectrophotometric assay of chloramine-T using sulfanilamide

A new spectrophotometric method for the assay of very small amounts of chloramine-T has been developed using sulfanilamide. This method is simple and accurate within the limits described.     

Cervical Precancer Detection Using a Multivariate Statistical Algorithm Based on Laser-Induced Fluorescence Spectra at Multiple Excitation Wavelengths

Abstract— A portable fluorimeter was developed and utilized to acquire fluorescence spectra from 381 cervical sites in 95 patients at 337, 380 and 460 nm excitation immediately prior to colposcopy. A multivariate statistical algorithm was used to extract clinically useful information from tissue spectra acquired in vivo. Two full-parameter algorithms were developed using tissue fluorescence emission spectra at all three excitation wavelengths (161 excitation-emission wavelength pairs) for cervical precancer (squamous intraepithelial lesion [SIL]) detection: a screening algorithm that discriminates between SIL and non-SIL with a sensitivity of 82 ± 1.4% and specificity of 68 ± 0.0%, and a diagnostic algorithm that differentiates high-grade SIL from non-high-grade SIL with a sensitivity and specificity of 79 ± 2% and 78 ± 6%, respectively. Multivariate statistical analysis was also employed to reduce the number of fluorescence excitation-emission wavelength pairs needed to redevelop algorithms that demonstrate a minimum decrease in classification accuracy. Two reduced-parameter algorithms that employ fluorescence intensities at only 15 excitation-emission wavelength pairs were developed: the screening algorithm differentiates SIL from non-SIL with a sensitivity of 84 ± 1.5% and specificity of 65 ± 2% and the diagnostic algorithm discriminates high-grade SIL from non-high-grade SIL with a sensitivity and specificity of 78 ± 0.7% and 74 ± 2%, respectively. Both the full-parameter and reduced-parameter screening algorithms discriminate between SIL and non-SIL with a similar specificity (±5%) and a substantially improved sensitivity relative to Pap smear screening. A comparison of the full-parameter and reduced-parameter diagnostic algorithms to colposcopy in expert hands indicates that all three have a very similar sensitivity and specificity for differentiating high-grade SIL from non-high-grade SIL.     

Extraction and extraction chromatographic separation of minor actinides from sulphate bearing high level waste solutions using CMPO

Bench-Scale studies on the partitioning and recovery of minoractinides from the actual and synthetic sulphate-bearing high level waste (SBHLW) solutions have been carried out by giving two contacts with 30% TBP to deplete uranium content followed by four contacts with 0.2M CMPO+1.2M TBP in dodecane. The acidity of the SBHLW solutions was about 0.3M. In the case of actual SBHLW, the final raffinate contained about 0.4% -activity originally present in the HLW, whereas with synthetic SBHLW the -activity was reduced to the background level.¹⁴⁴Ce is extracted almost quantitative in the CMPO phase,¹⁰⁶Ru about 12% and¹³⁷Cs is practically not extracted at all. The extraction chromatographic column studies with synthetic SBHLW (aftertwo TBP contacts) has shown that large volume of waste solutions could be passed through the column without break-through of actinide metal ions. Using 0.04M HNO₃>99% Am(III) and rare earths could be eluted/stripped. Similarly >99% Pu(IV) and U(VI) could be eluted.stripped using 0.01M oxalic acid and 0.25M sodium carbonate, respectively. In the presence of 0.16M SO ₄ ^2– (in the SBHLW) the complex ions AmSO ₄ ⁺ , UO₂SO₄, PuSO ₄ ²⁺ and Pu(SO₄)₂ were formed in the aqueous phase but the species extracted into the organic phase (CMPO+TBP) were only the nitrato complexes Am(NO₃)₃·3CMPO, UO₂(NO₃)₂·2CMPO and Pu(NO₃)₄·2CMPO. A scheme for the recovery of minor actinides from SBHLW solution with two contacts of 30% TBP followed by either solvent extraction or extraction chromatographic techniques has been proposed.